Lily has $3$ gallons of milk and gives $\frac{12}{5}$ gallons to James. What fraction of a gallon does she have left?
We want to subtract $\frac{12}{5}$ from $3$. To do this, we get a common denominator of $5$. We get  $$3-\frac{12}{5} = \frac{15}{5}-\frac{12}{5}=\frac{15-12}{5}=\boxed{\frac{3}{5}}.$$